Finite Group Databasebeta

← Group #13170508

Character table — Group #13170508

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162C163C164C165C166C167C168
size11112222222222224444444444446666666666666688889999121212121212121212121212121212121212121218181818181818183636363654541111222222222222444444444444666666666666668888999912121212121212121212121212121212121212121818181818181818363636365454
order12443336661212121212123336661212121212128888882424242424242424361212224424242424242424242424242424242424242424242244661212661212882244666666121212121212666666121212121212888888242424242424242466121222442424242424242424242424242424242424242424224466121266121288
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111111111111111111111111111-1-111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1111111-1-1-1-11111-1-1-1-111-1-111111111-1-1-1-111111-11-1-1-1-1-11-11-1-1-1111111111111111111111111111111-1-1111111-1-1-1-11111-1-1-1-111-1-111111111-1-1-1-111111-11-1-1-1-1-11-11-1-1-1
χ4111111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-11-1-1-1-1-11-1111111111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-11-1-1-1-1-11-1111
χ51111111111111111111111111111-1-11111-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-111111111-11-11-1-1-1-1-11-11-1-11111111111111111111111111111-1-11111-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-111111111-11-11-1-1-1-1-11-11-1-1
χ61111111111111111111111111111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11-11-1-1-1-1-11-11-1111111111111111111111111111111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11-11-1-1-1-1-11-11-111
χ71111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1
χ911-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1i−ii−ii−iii−i−iii−i−i11-1-111-1-1i−ii−iii−i−iii−i−iii−i−iii−i−i11-1-111-1-111-1-1i−i11-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1i−ii−ii−iii−i−iii−i−i11-1-111-1-1i−ii−iii−i−iii−i−iii−i−iii−i−i11-1-111-1-111-1-1i−i
χ1011-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1i−ii−i−iiii−i−iii−i−i11-1-111-1-1i−ii−i−i−iiiii−i−iii−i−i−i−iii-1-11111-1-1-1-111−ii11-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1i−ii−i−iiii−i−iii−i−i11-1-111-1-1i−ii−i−i−iiiii−i−iii−i−i−i−iii-1-11111-1-1-1-111−ii
χ1111-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1i−i−iii−iii−i−i−i−iii11-1-1-1-111i−i−iiii−i−iii−i−i−i−iiiii−i−i1-1-11-1-1111-1-11−ii11-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1i−i−iii−iii−i−i−i−iii11-1-1-1-111i−i−iiii−i−iii−i−i−i−iiiii−i−i1-1-11-1-1111-1-11−ii
χ1211-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1i−i−ii−iiii−i−i−i−iii11-1-1-1-111i−i−ii−i−iiiii−i−i−i−iii−i−iii-111-1-1-111-111-1i−i11-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1i−i−ii−iiii−i−i−i−iii11-1-1-1-111i−i−ii−i−iiiii−i−i−i−iii−i−iii-111-1-1-111-111-1i−i
χ1311-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1−iii−ii−i−i−iiiii−i−i11-1-1-1-111−iii−iii−i−i−i−iiiii−i−iii−i−i-111-1-1-111-111-1−ii11-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1−iii−ii−i−i−iiiii−i−i11-1-1-1-111−iii−iii−i−i−i−iiiii−i−iii−i−i-111-1-1-111-111-1−ii
χ1411-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1−iii−i−ii−i−iiiii−i−i11-1-1-1-111−iii−i−i−iii−i−iiiii−i−i−i−iii1-1-11-1-1111-1-11i−i11-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1−iii−i−ii−i−iiiii−i−i11-1-1-1-111−iii−i−i−iii−i−iiiii−i−i−i−iii1-1-11-1-1111-1-11i−i
χ1511-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1−ii−iii−i−i−iii−i−iii11-1-111-1-1−ii−iiii−i−i−i−iii−i−iiiii−i−i-1-11111-1-1-1-111i−i11-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1−ii−iii−i−i−iii−i−iii11-1-111-1-1−ii−iiii−i−i−i−iii−i−iiiii−i−i-1-11111-1-1-1-111i−i
χ1611-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1−ii−ii−ii−i−iii−i−iii11-1-111-1-1−ii−ii−i−iii−i−iii−i−iii−i−iii11-1-111-1-111-1-1−ii11-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1−ii−ii−ii−i−iii−i−iii11-1-111-1-1−ii−ii−i−iii−i−iii−i−iii−i−iii11-1-111-1-111-1-1−ii
χ17222222-122-12222-1-12-1-12-1-122-1-1-1-100222200002222-1-1-1-1000000-1-12-12-10000-1-1-1-1-1-1-1-1020200000-10-100222222-122-12222-1-12-1-12-1-122-1-1-1-100222200002222-1-1-1-1000000-1-12-12-10000-1-1-1-1-1-1-1-1020200000-10-100
χ18222222-122-12222-1-12-1-12-1-122-1-1-1-10022-2-200002222-1-1-1-1000000-1-1-21-210000-1-1-1-111110-20-20000010100222222-122-12222-1-12-1-12-1-122-1-1-1-10022-2-200002222-1-1-1-1000000-1-1-21-210000-1-1-1-111110-20-20000010100
χ19222222-122-12222-1-12-1-12-1-122-1-1-1-100-2-2220000-2-2-2-2-1-1-1-1000000112-12-100001111-1-1-1-10-20-20000010100222222-122-12222-1-12-1-12-1-122-1-1-1-100-2-2220000-2-2-2-2-1-1-1-1000000112-12-100001111-1-1-1-10-20-20000010100
χ20222222-122-12222-1-12-1-12-1-122-1-1-1-100-2-2-2-20000-2-2-2-2-1-1-1-100000011-21-21000011111111020200000-10-100222222-122-12222-1-12-1-12-1-122-1-1-1-100-2-2-2-20000-2-2-2-2-1-1-1-100000011-21-21000011111111020200000-10-100
χ2122222-122-1222-1-122-12-1-12-1-1-122-1-122002222220000-1-1-1-10000-1-100-12-12-1-1-1-10000-1-1-1-120200000-10-100022222-122-1222-1-122-12-1-12-1-1-122-1-122002222220000-1-1-1-10000-1-100-12-12-1-1-1-10000-1-1-1-120200000-10-1000
χ2222222-122-1222-1-122-12-1-12-1-1-122-1-12200-2-222220000-1-1-1-10000-1-1001-21-2-1-1-1-100001111-20-20000010100022222-122-1222-1-122-12-1-12-1-1-122-1-12200-2-222220000-1-1-1-10000-1-1001-21-2-1-1-1-100001111-20-200000101000
χ2322222-122-1222-1-122-12-1-12-1-1-122-1-1-2-20022-2-2-2-20000-1-1-1-100001100-12-1211110000-1-1-1-1-20-20000010100022222-122-1222-1-122-12-1-12-1-1-122-1-1-2-20022-2-2-2-20000-1-1-1-100001100-12-1211110000-1-1-1-1-20-200000101000
χ2422222-122-1222-1-122-12-1-12-1-1-122-1-1-2-200-2-2-2-2-2-20000-1-1-1-1000011001-21-211110000111120200000-10-100022222-122-1222-1-122-12-1-12-1-1-122-1-1-2-200-2-2-2-2-2-20000-1-1-1-1000011001-21-211110000111120200000-10-1000
χ252222-122-122-1-12222-1-12-1-12-1-1-1-122222200-1-1-1-1-1-1-1-1-1-1-1-1222222220000-1-1-1-1-1-1-1-100000000-1-1-1-10000002222-122-122-1-12222-1-12-1-12-1-1-1-122222200-1-1-1-1-1-1-1-1-1-1-1-1222222220000-1-1-1-1-1-1-1-100000000-1-1-1-1000000
χ262222-122-122-1-12222-1-12-1-12-1-1-1-12222-2-200-1-1-1-11111-1-1-1-1-2-2-2-222-2-20000-1-1-1-111110000000011110000002222-122-122-1-12222-1-12-1-12-1-1-1-12222-2-200-1-1-1-11111-1-1-1-1-2-2-2-222-2-20000-1-1-1-11111000000001111000000
χ272222-122-122-1-12222-1-12-1-12-1-1-1-122-2-222001111-1-1-1-1-1-1-1-1-2-2-2-2-2-22200001111-1-1-1-10000000011110000002222-122-122-1-12222-1-12-1-12-1-1-1-122-2-222001111-1-1-1-1-1-1-1-1-2-2-2-2-2-22200001111-1-1-1-1000000001111000000
χ282222-122-122-1-12222-1-12-1-12-1-1-1-122-2-2-2-20011111111-1-1-1-12222-2-2-2-200001111111100000000-1-1-1-10000002222-122-122-1-12222-1-12-1-12-1-1-1-122-2-2-2-20011111111-1-1-1-12222-2-2-2-200001111111100000000-1-1-1-1000000
χ2922-2-222-122-1-2-2-2-2112-1-12-1-1-2-21111002i−2i2i−2i00002i2i−2i−2i-1-111000000−ii2i−i−2ii0000−i−iii−i−iii020-200000-1010022-2-222-122-1-2-2-2-2112-1-12-1-1-2-21111002i−2i2i−2i00002i2i−2i−2i-1-111000000−ii2i−i−2ii0000−i−iii−i−iii020-200000-10100
χ3022-2-222-122-1-2-2-2-2112-1-12-1-1-2-21111002i−2i−2i2i00002i2i−2i−2i-1-111000000−ii−2ii2i−i0000−i−iiiii−i−i0-2020000010-10022-2-222-122-1-2-2-2-2112-1-12-1-1-2-21111002i−2i−2i2i00002i2i−2i−2i-1-111000000−ii−2ii2i−i0000−i−iiiii−i−i0-2020000010-100
χ3122-2-222-122-1-2-2-2-2112-1-12-1-1-2-2111100−2i2i2i−2i0000−2i−2i2i2i-1-111000000i−i2i−i−2ii0000ii−i−i−i−iii0-2020000010-10022-2-222-122-1-2-2-2-2112-1-12-1-1-2-2111100−2i2i2i−2i0000−2i−2i2i2i-1-111000000i−i2i−i−2ii0000ii−i−i−i−iii0-2020000010-100
χ3222-2-222-122-1-2-2-2-2112-1-12-1-1-2-2111100−2i2i−2i2i0000−2i−2i2i2i-1-111000000i−i−2ii2i−i0000ii−i−iii−i−i020-200000-1010022-2-222-122-1-2-2-2-2112-1-12-1-1-2-2111100−2i2i−2i2i0000−2i−2i2i2i-1-111000000i−i−2ii2i−i0000ii−i−iii−i−i020-200000-10100
χ3322-2-22-122-12-2-211-2-2-12-1-12-111-2-2112i−2i002i−2i2i2i−2i−2i0000-1-1110000−ii00−i2ii−2i−i−iii0000−i−iii20-200000-10100022-2-22-122-12-2-211-2-2-12-1-12-111-2-2112i−2i002i−2i2i2i−2i−2i0000-1-1110000−ii00−i2ii−2i−i−iii0000−i−iii20-200000-101000
χ3422-2-22-122-12-2-211-2-2-12-1-12-111-2-2112i−2i00−2i2i2i2i−2i−2i0000-1-1110000−ii00i−2i−i2i−i−iii0000ii−i−i-2020000010-100022-2-22-122-12-2-211-2-2-12-1-12-111-2-2112i−2i00−2i2i2i2i−2i−2i0000-1-1110000−ii00i−2i−i2i−i−iii0000ii−i−i-2020000010-1000
χ3522-2-22-122-12-2-211-2-2-12-1-12-111-2-211−2i2i002i−2i−2i−2i2i2i0000-1-1110000i−i00−i2ii−2iii−i−i0000−i−iii-2020000010-100022-2-22-122-12-2-211-2-2-12-1-12-111-2-211−2i2i002i−2i−2i−2i2i2i0000-1-1110000i−i00−i2ii−2iii−i−i0000−i−iii-2020000010-1000
χ3622-2-22-122-12-2-211-2-2-12-1-12-111-2-211−2i2i00−2i2i−2i−2i2i2i0000-1-1110000i−i00i−2i−i2iii−i−i0000ii−i−i20-200000-10100022-2-22-122-12-2-211-2-2-12-1-12-111-2-211−2i2i00−2i2i−2i−2i2i2i0000-1-1110000i−i00i−2i−i2iii−i−i0000ii−i−i20-200000-101000
χ3722-2-2-122-12211-2-2-2-2-1-12-1-121111-2-22i−2i2i−2i00−i−iii−i−iii-1-11122-2-22i−2i2i−2i0000−i−iii−i−iii00000000-1-11100000022-2-2-122-12211-2-2-2-2-1-12-1-121111-2-22i−2i2i−2i00−i−iii−i−iii-1-11122-2-22i−2i2i−2i0000−i−iii−i−iii00000000-1-111000000
χ3822-2-2-122-12211-2-2-2-2-1-12-1-121111-2-22i−2i−2i2i00−i−iiiii−i−i-1-111-2-2222i−2i−2i2i0000−i−iiiii−i−i0000000011-1-100000022-2-2-122-12211-2-2-2-2-1-12-1-121111-2-22i−2i−2i2i00−i−iiiii−i−i-1-111-2-2222i−2i−2i2i0000−i−iiiii−i−i0000000011-1-1000000
χ3922-2-2-122-12211-2-2-2-2-1-12-1-121111-2-2−2i2i2i−2i00ii−i−i−i−iii-1-111-2-222−2i2i2i−2i0000ii−i−i−i−iii0000000011-1-100000022-2-2-122-12211-2-2-2-2-1-12-1-121111-2-2−2i2i2i−2i00ii−i−i−i−iii-1-111-2-222−2i2i2i−2i0000ii−i−i−i−iii0000000011-1-1000000
χ4022-2-2-122-12211-2-2-2-2-1-12-1-121111-2-2−2i2i−2i2i00ii−i−iii−i−i-1-11122-2-2−2i2i−2i2i0000ii−i−iii−i−i00000000-1-11100000022-2-2-122-12211-2-2-2-2-1-12-1-121111-2-2−2i2i−2i2i00ii−i−iii−i−i-1-11122-2-2−2i2i−2i2i0000ii−i−iii−i−i00000000-1-111000000
χ412-22i−2i222-2-2-22i−2i2i−2i2i−2i222-2-2-22i−2i2i−2i2i−2i000000000000002-22i−2i2-22i−2i0000000000000000000000002-22i−2i0000002-22i−2i222-2-2-22i−2i2i−2i2i−2i222-2-2-22i−2i2i−2i2i−2i000000000000002-22i−2i2-22i−2i0000000000000000000000002-22i−2i000000
χ422-22i−2i222-2-2-22i−2i2i−2i2i−2i222-2-2-22i−2i2i−2i2i−2i000000000000002-22i−2i-22−2i2i000000000000000000000000-22−2i2i0000002-22i−2i222-2-2-22i−2i2i−2i2i−2i222-2-2-22i−2i2i−2i2i−2i000000000000002-22i−2i-22−2i2i000000000000000000000000-22−2i2i000000
χ432-22i−2i-1221-2-2−ii2i−2i2i−2i-1-1211-2−ii−ii2i−2i000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13-11−ii2-22i−2i00000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ1300000000-11−ii0000002-22i−2i-1221-2-2−ii2i−2i2i−2i-1-1211-2−ii−ii2i−2i000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13-11−ii2-22i−2i00000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ1300000000-11−ii000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.